两类含非线性传染率的传染病模型的定性分析  

Qualitative Analysis of Nonlinear Incidence Rate for Two Epidemic Models

作　　者：李建全[1] 王拉娣[2] 杨友社[1] 

机构地区：[1]空军工程大学电讯工程学院,陕西西安710077 [2]上海大学数学系

出　　处：《空军工程大学学报（自然科学版）》2004年第1期84-88,共5页Journal of Air Force Engineering University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(19971066)

摘　　要：讨论了两类具有非线性传染率的传染病模型,确定了各类平衡点存在的阈值条件,通过构造Dulac函数和Liapunov函数,得到了无病平衡点和地方病平衡点全局渐近稳定的充要条件。Two epidemic models with nonlinear incidence rate are investigated in this paper, and the threshold of the existence of various equilibrium is found. By means of constructing Dulac function and Liapunov function, the necessary and sufficient conditions that guarantee the global asymptotic stability of disease - free equilibrium and endemic equilibrium are obtained.

关 键 词：传染病模型 阈值 定性分析 非线性传染率 无病平衡点 地方病平衡点 全局渐近稳定 

分 类 号：R181.2[医药卫生—流行病学] O175.12[医药卫生—公共卫生与预防医学]